Again, I just re-watched several of the films -- Captain America - First Avenger -- and he wasn't well funded and really struggled. Hardly rich. In fact they treated him as a prop. He's bullied through the first thirty minutes of the film. Go re-watch it.

And Thor? That's a Shakespearean dram about hubris. His father takes away everything from him to teach him to value life.

Doctor Strange? He's dead broke by the time he seeks out mystic arts, has no money, no funding. And gives up his dream of regaining his hands to protect the mystic realm.

Iron Man -- he's captured by terrorists.

The problem is you're trying to watch the Avengers as a stand-a-lone and it's not. You really have to look at all the movies together as a whole. I was referencing the film plots not the comics. It would be like watching and judging Buffy as a hero based on well Chosen or one isolated episode.
Or Spiderman based on his role in the Avengers solely.